Leading strategies in competitive on-line prediction

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.Comment: 20 pages; a conference version is to appear in the ALT'2006 proceeding

On-line regression competitive with reproducing kernel Hilbert spaces

We consider the problem of on-line prediction of real-valued labels, assumed bounded in absolute value by a known constant, of new objects from known labeled objects. The prediction algorithm's performance is measured by the squared deviation of the predictions from the actual labels. No stochastic assumptions are made about the way the labels and objects are generated. Instead, we are given a benchmark class of prediction rules some of which are hoped to produce good predictions. We show that for a wide range of infinite-dimensional benchmark classes one can construct a prediction algorithm whose cumulative loss over the first N examples does not exceed the cumulative loss of any prediction rule in the class plus O(sqrt(N)); the main differences from the known results are that we do not impose any upper bound on the norm of the considered prediction rules and that we achieve an optimal leading term in the excess loss of our algorithm. If the benchmark class is "universal" (dense in the class of continuous functions on each compact set), this provides an on-line non-stochastic analogue of universally consistent prediction in non-parametric statistics. We use two proof techniques: one is based on the Aggregating Algorithm and the other on the recently developed method of defensive forecasting.Comment: 37 pages, 1 figur

Nutrient levels and trade-offs control diversity in a serial dilution ecosystem

Microbial communities feature an immense diversity of species and this diversity is linked with outcomes ranging from ecosystem stability to medical prognoses. Yet the mechanisms underlying microbial diversity are under debate. While simple resource-competition models don't allow for coexistence of a large number of species, it was recently shown that metabolic trade-offs can allow unlimited diversity. Does this diversity persist with more realistic, intermittent nutrient supply? Here, we demonstrate theoretically that in serial dilution culture, metabolic trade-offs allow for high diversity. When a small amount of nutrient is supplied to each batch, the serial dilution dynamics mimic a chemostat-like steady state. If more nutrient is supplied, diversity depends on the amount of nutrient supplied due to an "early-bird" effect. The interplay of this effect with different environmental factors and diversity-supporting mechanisms leads to a variety of relationships between nutrient supply and diversity, suggesting that real ecosystems may not obey a universal nutrient-diversity relationship.Comment: Appendix follows main tex

Defensive forecasting for optimal prediction with expert advice

The method of defensive forecasting is applied to the problem of prediction with expert advice for binary outcomes. It turns out that defensive forecasting is not only competitive with the Aggregating Algorithm but also handles the case of "second-guessing" experts, whose advice depends on the learner's prediction; this paper assumes that the dependence on the learner's prediction is continuous.Comment: 14 page

Vertical competition between manufacturers and retailers and upstream incentives to innovate and differentiate

Vertical competition, namely competition between retailers' store brands (or private labels) and manufacturers' brands has become a crucial factor of change of the competitive environment in several industries, particularly in the grocery and food industries. Despite the growing literature on the determinants of the phenomenon, one topic area regarding the impact of vertical competition on the upstream incentives to adopt non-price strategies such as product innovation as well as horizontal and vertical product differentiation has so far received little attention. An idea often put forward is that the increasing bargaining power of retailers and higher vertical competitive pressures can have negative effects on such incentives by lowering manufacturers' profits. On the other hand, there is a significant empirical evidence supporting the view that non-price strategies of product innovation and differentiation continue to play a key role and remain a crucial source of competitive advantages for several manufacturers. In this paper, we present a simple conceptual framework which allows us to focus on two hypotheses which interacting explain why the disincentive effects are not so obvious. The first hypothesis regards the existence of an inverse relationship between the strength of a given brand and the retail margin as suggested by Robert Steiner. Through a two-stage model in which manufacturers do not sell directly to final consumers and the retail industry is not perfectly competitive, Steiner argued persuasively that in such models leading brands in a product category yield lower retail margins than less strong brands. Retailers are forced to stock strong brands and therefore have relatively less bargaining power in negotiating wholesale prices. In addition, price competition among retailers is more intense on strong brands since consumers select these brands to form their perceptions of stores' price competitiveness and are ready to shift to lower price stores if retail price of these brands is not perceived as competitive. Thus, intensive intrabrand competitive pressures discipline retailers pricing policy on stronger manufacturer brands much more than on weaker brands. A key prediction of Steiner's two-stage model is that, since manufacturers' non-price strategies have a margin depressing impact which is additional to their direct demand - creating effect, manufacturers face greater incentives to invest in advertising and R&D. The second central hypothesis in our framework is that in a world of asymmetric brands and intense vertical competition there is a further mechanism at work due to retailers' delisting decisions. Given that retailers have to make room for their store brands at the point of sale, they have to readjust their assortments delisting some manufacturer brands. Retailers would like delisting strong brands given that the retailer's margin on these brands is lower. The problem is that strong brands can contrast vertical pressures better than weaker brands and cannot be delisted. In making shelf - space decisions, rational retailers will recognise that they can delist only the brands whose brand loyalty is lower than their store loyalty. On the contrary, retailers cannot delist brands for which brand loyalty is greater than store loyalty. This implies that manufacturer brands operate in a two- region environment. We call these two regions, respectively, the 'delisting' and 'no-delisting' region and show that the demarcation point between them is given by the level of retailer's store loyalty. By combining the Steiner's hypothesis with the mechanism of delisting, we argue that in a competitive environment characterized by vertical competition is at work a threshold effect which increases optimal 2 R&D and advertising expenditures. The intuition is that it is vital for manufacturers willing to remain sellers of branded products to keep brand loyalty of their brands at a level higher than retailer's store loyalty. And the only way to pursue this goal and avoid to be involved into the risk of being delisted is to boost brands. We also show that vertical competitive pressures are particularly strong on second- tier brands. A brief review of some recent patterns and stylised facts in the food industries and grocery channels consistent with these predictions conclude the paper.vertical competition, store brands, delisting, optimal advertising, Industrial Organization,

Market Structure, R&D and Advertising in the Pharmaceutical Industry

Recent developments in the literature on market structure have allowed the generation of a few key testable predictions from the theory of strategic behaviour. The seminal model considers one simple but general relationship, that between market structure and market size, focusing on the competitive roles of the endogenous sunk costs of advertising and/or research and development (R&D). Evidence presented in this case study, building on earlier econometric work, shows that such endogenous sunk costs do play a crucial role in the formation of market structure in the global pharmaceutical industry. ZUSAMMENFASSUNG - (Werbung, FuE und Marktstruktur in der pharmazeutischen Industrie) Jüngere Entwicklungen der Literatur zum Thema "Marktstruktur" ermöglichen es, robuste testbare Hypothesen aus der Theorie des strategischen Verhaltens abzuleiten. Das grundlegende industrieökonomische Modell geht von einer einfachen, aber allgemein gültigen Beziehung zwischen Konzentration und Marktgröße aus. Dabei wird insbesondere der Einfluß endogener versunkener Kosten für Werbung und/oder Forschung und Entwicklung (FuE) auf den Wettbewerb untersucht. Die empirischen Ergebnisse dieser Fallstudie zeigen, daß endogene versunkene Kosten tatsächlich eine entscheidende Rolle für die Herausbildung der Marktstruktur in der pharmazeutischen Industrie spielen. Die Ergebnisse zeigen jedoch auch, daß unternehmensspezifische Fähigkeiten geeignet sind, die Reaktionsweisen der Unternehmen im Wettbewerb zu erklären.market structure; advertising; R&D; pharmaceuticals